1 Labor Market Equilibrium

2 Overview In this section we want to explore what happens in a competitive labor market. Plus we will look at an application of this type of labor market.

3 Single competitive labor market If the whole economy comprises a single competitive labor market, then the wage and amount of labor employed is determined by the interaction of supply and demand. Then any one firm, or worker, is a wage taker. This means the worker or the firm can not determine the wage alone. Again, the wage is set by the interaction of all parties concerned. Recall from our earlier work that a profit maximizing firm hirers labor up to the point where the value of the marginal product is equal to the wage.

4 Single labor market E $ W* E* S D In the market we get W* and E*. Each firm takes W* and hires what they want and when you add that across firms you get E*, which is just the total supplied.

5 Equilibrium W* is the equilibrium wage because at this wage both suppliers and demanders obtain the desired amount. At wages higher than W* an equilibrium would not exist because at those wages the quantity supplied is much higher than the quantity demanded – an excess supply. All those willing to supply do not get to trade because there are too few buyers. Since this excess supply will encourage suppliers to change by lowering the wage at which many will work, the initial high wage (relative to the equilibrium) will not last and will change to the equilibrium wage.

6 More equilibrium At wages lower than W* an equilibrium would not exist because at those wages the quantity supplied is much lower than the quantity demanded – an excess demand. All those demanding do not get to trade because there are too few sellers. Since this excess demand will encourage demanders to change by raising the wage which they will pay for work, the initial low wage (relative to the equilibrium) will not last and will change to the equilibrium wage.

Basic Minimum Wage Model

Basic economic model of minimum wage impact wage employment S D wbar W* Ebar E* Es

Basic model Assumptions - all firms comply with the law and all workers in the economy are covered by the law, meaning their wage can be no lower than the legal minimum. In the graph W* is called too low and thus a minimum is enacted. wbar is an example of an effective minimum wage because the market price can not occur. (is a wage lower than w* an effective minimum?) At wbar the Qs = Es and the Qd = Ebar and thus Es - Ebar = surplus or unemployment.

implications Now, since Es - Ebar = surplus or unemployment, we have Es - Ebar = (Es –E*) + (E* - Ebar). The unemployment created by the minimum wage is made up of two components: Es – E* is the unemployment that results because a higher wage attracts more workers, even though firms do not want to hire them; E* - Ebar is the unemployment from those who actually had work before the minimum, but lose their job due to the minimum wage. Now, those that still work, Ebar, get the higher wage and make more income.

non-compliance All firms do not comply with the law. If and when they get caught the “guilty” firms typically have to pay workers the money they did not originally pay them. So in a way you could say non-compliant firms are getting an interest free loan from the employees they are with-holding from. Plus, the unemployment that would happen if all complied does not occur. In other words, the amount of unemployed is less when there is non-compliance.

what if all workers are not covered by law? In the real world all workers are not covered by the law. In other words, some types of jobs do not require a minimum be paid. We will want to explore what can happen in the sectors that are covered by the law and the sectors that are NOT covered by the law. But let’s digress for a minute. Say if I flip a coin and it comes up heads I will give you a dollar, but if it comes up tails you will give me a dollar. (By the way, if you are ever offered this bet, please only accept it if you can use your coin and you flip the coin.) The expected win is.5(1) +.5(-1) = 0, or in general the probability of an outcome times its outcome, summed across all outcomes.

covered sector Look back at the graph I had at the beginning of this section. But, now consider it only the sector that is covered by the minimum wage. Say π is the probability you still have a job after the minimum wage is legislated. Thus (1- π) is the probability you do not have a job. The expected wage is then π(wbar) + (1 - π)(0) = πWbar.

uncovered sector If a worker goes to the uncovered sector then the wage is certain. Call this wage Wu. Then the expected wage in the uncovered sector is the certain wage Wu. Next let’s explore what might happen if the expected wage in each sector is not the same. As we do this consider the following two ideas. 1) Displaced workers in the covered can leave the covered market and enter the uncovered market, pushing the uncovered market wage down. 2) Workers in the uncovered market may leave for the covered market in hopes of getting a job there, pushing the uncovered wage up.

Say πwbar > Wu This condition means people expect to make more in the covered market than in the uncovered market. Workers move toward the covered market, lowering π and raising Wu. So, the inequality can not last.

Say πwbar < Wu This condition means people expect to make more in the uncovered market than in the covered market. Workers would move toward the uncovered market, raising π and lowering Wu. So again, the inequality can not last. So what is the moral of this story? The expected wage is the same in each market.